soaproot
@soaproot.sfba.social.ap.brid.gy
Also known.as: Jim Kingdon. Interested in: formal mathematics, software development, dance (especially country-western and #MorrisDancing, but many kinds), plants […]
[bridged from https://sfba.social/@soaproot on the fediverse by https://fed.brid.gy/ ]
[bridged from https://sfba.social/@soaproot on the fediverse by https://fed.brid.gy/ ]
This is a 🧵 about the Dedekind cut construction of real numbers in #constructivemathematics , particularly two technical details. The first has to do with defining additive inverse and multiplication, when we can't use excluded middle for things like "is a real number positive or not?". The […]
Original post on sfba.social
sfba.social
December 31, 2025 at 6:03 PM
This is a 🧵 about the Dedekind cut construction of real numbers in #constructivemathematics , particularly two technical details. The first has to do with defining additive inverse and multiplication, when we can't use excluded middle for things like "is a real number positive or not?". The […]
Reposted by soaproot
@williampietri If you want one thing to read, go for Andrej Bauer's "Five stages of accepting constructive mathematics," Bulletin (New Series) of the American Mathematical Society, 54:481-498 (2017), http://dx.doi.org/10.1090/bull/1556 (open access). There's one or two sections you (or even me […]
Original post on sfba.social
sfba.social
December 19, 2025 at 9:03 PM
@williampietri If you want one thing to read, go for Andrej Bauer's "Five stages of accepting constructive mathematics," Bulletin (New Series) of the American Mathematical Society, 54:481-498 (2017), http://dx.doi.org/10.1090/bull/1556 (open access). There's one or two sections you (or even me […]
Reposted by soaproot
@williampietri This one might be a bit hard to explain except in a certain mathematical niche, but the last few months have been great for my constructive set theory proofs and webpages.
See https://us.metamath.org/ileuni/mmil.html#flavors and the following two sections ("A note on existence" […]
See https://us.metamath.org/ileuni/mmil.html#flavors and the following two sections ("A note on existence" […]
Original post on sfba.social
sfba.social
December 18, 2025 at 5:41 PM
@williampietri This one might be a bit hard to explain except in a certain mathematical niche, but the last few months have been great for my constructive set theory proofs and webpages.
See https://us.metamath.org/ileuni/mmil.html#flavors and the following two sections ("A note on existence" […]
See https://us.metamath.org/ileuni/mmil.html#flavors and the following two sections ("A note on existence" […]
Reposted by soaproot
My former PhD student Ho Weng Kin didn't manage to attend in person, but he gave a talk online.
He spoke about an open problem, which, he reminded me, I told him to spend only 5% of this time thinking during his PhD, 20 years ago, no matter how obsessed he was with the problem then.
The […]
He spoke about an open problem, which, he reminded me, I told him to spend only 5% of this time thinking during his PhD, 20 years ago, no matter how obsessed he was with the problem then.
The […]
Original post on mathstodon.xyz
mathstodon.xyz
December 18, 2025 at 7:11 PM
My former PhD student Ho Weng Kin didn't manage to attend in person, but he gave a talk online.
He spoke about an open problem, which, he reminded me, I told him to spend only 5% of this time thinking during his PhD, 20 years ago, no matter how obsessed he was with the problem then.
The […]
He spoke about an open problem, which, he reminded me, I told him to spend only 5% of this time thinking during his PhD, 20 years ago, no matter how obsessed he was with the problem then.
The […]
Reposted by soaproot
Take an integer N which is not a multiple of 10.
There is some multiple of N containing only the digits 1, 2, 3, 4, and 5.
https://www.johndcook.com/blog/2025/12/16/multiples-with-no-large-digits/
There is some multiple of N containing only the digits 1, 2, 3, 4, and 5.
https://www.johndcook.com/blog/2025/12/16/multiples-with-no-large-digits/
Multiples with no large digits
Here’s a curious theorem I stumbled across recently [1]. Take an integer _N_ which is not a multiple of 10. Then there is some multiple of _N_ which only contains the digits 1, 2, 3, 4, and 5.
For example, my business phone number 8324228646 has a couple 8s and a couple 6s. But
6312 × 8324228646 = 52542531213552
which contains only digits 1 through 5.
For a general base _b_ , let _p_ be the smallest prime factor of _b_. Then for every integer _N_ that is not a multiple of _b_ , there is some multiple of _N_ whose base _b_ representation contains only the digits 1, 2, 3, …, _b_ /_p_.
This means that for every number _N_ that is not a multiple of 16, there is some _k_ such that the hex representation of _kN_ contains only the digits 1 through 8. For example, if we take the magic number at the beginning of every Java class file, 0xCAFEBABE, we find
1341 × CAFEBABEhex = 42758583546hex.
In the examples above, we’re looking for multiple containing only half the possible digits. If the largest prime dividing the base is larger than 2 then we can find a multiples with digits in a smaller range. For example, in base 35 we can find a multiple containing only the digits 1 through 7.
[1] Daniel Sitaru and Leonard Giugiuc. Sum of powers of the sides of a triangle. The American Mathematical Monthly, Vol. 126, No. 2 (February 2019), p. 188
www.johndcook.com
December 16, 2025 at 3:57 PM
Take an integer N which is not a multiple of 10.
There is some multiple of N containing only the digits 1, 2, 3, 4, and 5.
https://www.johndcook.com/blog/2025/12/16/multiples-with-no-large-digits/
There is some multiple of N containing only the digits 1, 2, 3, 4, and 5.
https://www.johndcook.com/blog/2025/12/16/multiples-with-no-large-digits/
Sleigh bells ring, are you listening?
In the lane, snow is glistening
A beautiful sight
We're happy tonight
Tooting on a winter Mastodon
Gone away is the bluebird
Here to stay is a pachyderm
To sing a love song
While we stroll along
Tooting on a winter Mastodon
In the meadow, we can build a […]
In the lane, snow is glistening
A beautiful sight
We're happy tonight
Tooting on a winter Mastodon
Gone away is the bluebird
Here to stay is a pachyderm
To sing a love song
While we stroll along
Tooting on a winter Mastodon
In the meadow, we can build a […]
Original post on sfba.social
sfba.social
December 16, 2025 at 6:09 AM
Sleigh bells ring, are you listening?
In the lane, snow is glistening
A beautiful sight
We're happy tonight
Tooting on a winter Mastodon
Gone away is the bluebird
Here to stay is a pachyderm
To sing a love song
While we stroll along
Tooting on a winter Mastodon
In the meadow, we can build a […]
In the lane, snow is glistening
A beautiful sight
We're happy tonight
Tooting on a winter Mastodon
Gone away is the bluebird
Here to stay is a pachyderm
To sing a love song
While we stroll along
Tooting on a winter Mastodon
In the meadow, we can build a […]
Reposted by soaproot
A thread about "recursion versus induction".
This is about a beautiful idea discovered by Per Martin-Löf in his now known as Martin-Löf type theory, or MLTT.
Suppose you want to define a function f : ℕ → A.
One possibility is that we have an element a₀ : A and a function s : A → A, and then […]
This is about a beautiful idea discovered by Per Martin-Löf in his now known as Martin-Löf type theory, or MLTT.
Suppose you want to define a function f : ℕ → A.
One possibility is that we have an element a₀ : A and a function s : A → A, and then […]
Original post on mathstodon.xyz
mathstodon.xyz
December 11, 2025 at 10:06 PM
A thread about "recursion versus induction".
This is about a beautiful idea discovered by Per Martin-Löf in his now known as Martin-Löf type theory, or MLTT.
Suppose you want to define a function f : ℕ → A.
One possibility is that we have an element a₀ : A and a function s : A → A, and then […]
This is about a beautiful idea discovered by Per Martin-Löf in his now known as Martin-Löf type theory, or MLTT.
Suppose you want to define a function f : ℕ → A.
One possibility is that we have an element a₀ : A and a function s : A → A, and then […]
RE: https://tech.lgbt/@libsteve/115611585076070209
Anyone on #librarians or #bookstodon who knows something about Library of Congress classification willing to take a few questions from @libsteve ?
Anyone on #librarians or #bookstodon who knows something about Library of Congress classification willing to take a few questions from @libsteve ?
tech.lgbt
November 26, 2025 at 6:00 PM
RE: https://tech.lgbt/@libsteve/115611585076070209
Anyone on #librarians or #bookstodon who knows something about Library of Congress classification willing to take a few questions from @libsteve ?
Anyone on #librarians or #bookstodon who knows something about Library of Congress classification willing to take a few questions from @libsteve ?
Reposted by soaproot
Fediverse admin, moderator and community manager efforts resolve the overwhelming majority of issues before most are even aware of them.
Let's hold moderation to high standards, while also extending the respect and support these volunteers deserve.
Send your mod team some love today. They’ve […]
Let's hold moderation to high standards, while also extending the respect and support these volunteers deserve.
Send your mod team some love today. They’ve […]
Original post on mastodon.iftas.org
mastodon.iftas.org
November 4, 2025 at 1:39 PM
Fediverse admin, moderator and community manager efforts resolve the overwhelming majority of issues before most are even aware of them.
Let's hold moderation to high standards, while also extending the respect and support these volunteers deserve.
Send your mod team some love today. They’ve […]
Let's hold moderation to high standards, while also extending the respect and support these volunteers deserve.
Send your mod team some love today. They’ve […]
Metazooa
Become an evolutionary detective to find the Mystery Animal!
metazooa.com
October 24, 2025 at 2:13 AM
🐗 Animal #776 🐃
I figured it out in 5 guesses!
🟥🟧🟩🟩🟩
🔥 2 | Avg. Guesses: 5.8
https://metazooa.com
#metazooa
I figured it out in 5 guesses!
🟥🟧🟩🟩🟩
🔥 2 | Avg. Guesses: 5.8
https://metazooa.com
#metazooa
Metazooa
Become an evolutionary detective to find the Mystery Animal!
metazooa.com
September 14, 2025 at 3:08 PM
🐗 Animal #776 🐃
I figured it out in 5 guesses!
🟥🟧🟩🟩🟩
🔥 2 | Avg. Guesses: 5.8
https://metazooa.com
#metazooa
I figured it out in 5 guesses!
🟥🟧🟩🟩🟩
🔥 2 | Avg. Guesses: 5.8
https://metazooa.com
#metazooa
Reposted by soaproot
@llewelly @soaproot important to note that fossil pseudofeces is very different from the equally entertaining topic of pseudo fossil feces https://theplosblog.plos.org/2014/07/pseudo-poo-glitters-isnt-fecal-gold/
theplosblog.plos.org
September 6, 2025 at 3:22 PM
@llewelly @soaproot important to note that fossil pseudofeces is very different from the equally entertaining topic of pseudo fossil feces https://theplosblog.plos.org/2014/07/pseudo-poo-glitters-isnt-fecal-gold/
At the California Science Center museum and just found some new (to me) #clamfacts . According to Wikipedia this species lives at thousands of meters below the ocean's surface and gets nutrition from bacteria on its gills which can process hydrogen sulfide from deep sea vents.
August 21, 2025 at 8:16 PM
At the California Science Center museum and just found some new (to me) #clamfacts . According to Wikipedia this species lives at thousands of meters below the ocean's surface and gets nutrition from bacteria on its gills which can process hydrogen sulfide from deep sea vents.
I've posted about this a few times but let me try to do so more clearly. How do we, in #constructivemathematics , show that a set is countably infinite (that is, there is a bijection between our set and the set of natural numbers)? There's a theorem for this which is elegant and also handles […]
Original post on sfba.social
sfba.social
August 11, 2025 at 7:33 PM
I've posted about this a few times but let me try to do so more clearly. How do we, in #constructivemathematics , show that a set is countably infinite (that is, there is a bijection between our set and the set of natural numbers)? There's a theorem for this which is elegant and also handles […]
Reposted by soaproot
Y'all continue to be the most interested in clam facts by far of any socials I share on. I really admire ya. Stay curious!
August 1, 2025 at 9:24 PM
Y'all continue to be the most interested in clam facts by far of any socials I share on. I really admire ya. Stay curious!
Reposted by soaproot
I'm among those that have heard that a tsunami can be modelled as a soliton, but the authors of this article think that some important tsunamis of the past were not solitons and that you can just use the shallow water theory.
Solitons and Tsunamis […]
Solitons and Tsunamis […]
Original post on mathstodon.xyz
mathstodon.xyz
July 30, 2025 at 8:57 AM
I'm among those that have heard that a tsunami can be modelled as a soliton, but the authors of this article think that some important tsunamis of the past were not solitons and that you can just use the shallow water theory.
Solitons and Tsunamis […]
Solitons and Tsunamis […]
I'm writing about nonincreasing sequences of zeroes and ones. So you could have all zeroes, all ones, a one followed by zeroes, two ones followed by zeroes, etc. (Here a sequence is a function from ω, the set of natural numbers, to { 0 , 1 }). How many such sequences are there?
1/n
1/n
July 17, 2025 at 10:57 PM
I'm writing about nonincreasing sequences of zeroes and ones. So you could have all zeroes, all ones, a one followed by zeroes, two ones followed by zeroes, etc. (Here a sequence is a function from ω, the set of natural numbers, to { 0 , 1 }). How many such sequences are there?
1/n
1/n
Reposted by soaproot
Given the axioms of IZF set theory, define real numbers as Dedekind cuts, the complex exponential as the limit of an infinite series, and sine and cosine in terms of the complex exponential. Define τ to be the smallest positive real whose cosine is one. Define π to be the smallest positive real […]
Original post on sfba.social
sfba.social
June 28, 2024 at 1:55 PM
Given the axioms of IZF set theory, define real numbers as Dedekind cuts, the complex exponential as the limit of an infinite series, and sine and cosine in terms of the complex exponential. Define τ to be the smallest positive real whose cosine is one. Define π to be the smallest positive real […]
Reposted by soaproot
A counting problem on input size \\(N\\) where for all \\(N \geq 43632\\), we now know the answer \\(t(N)\\) satisfies
\\[ N/3 \leq t(N) \leq N/e \\]
and moreover, for all \\(N\neq 56\\), \\(t(N) \geq \lfloor N/3.5\rfloor\\), and the upper bound actually holds for all \\(N\neq 1,2,4\\) […]
\\[ N/3 \leq t(N) \leq N/e \\]
and moreover, for all \\(N\neq 56\\), \\(t(N) \geq \lfloor N/3.5\rfloor\\), and the upper bound actually holds for all \\(N\neq 1,2,4\\) […]
Original post on mathstodon.xyz
mathstodon.xyz
June 19, 2025 at 10:29 AM
A counting problem on input size \\(N\\) where for all \\(N \geq 43632\\), we now know the answer \\(t(N)\\) satisfies
\\[ N/3 \leq t(N) \leq N/e \\]
and moreover, for all \\(N\neq 56\\), \\(t(N) \geq \lfloor N/3.5\rfloor\\), and the upper bound actually holds for all \\(N\neq 1,2,4\\) […]
\\[ N/3 \leq t(N) \leq N/e \\]
and moreover, for all \\(N\neq 56\\), \\(t(N) \geq \lfloor N/3.5\rfloor\\), and the upper bound actually holds for all \\(N\neq 1,2,4\\) […]
Reposted by soaproot
In the ocean, if you build it, they will come. By "they" I mean the entire ecosystem! From oil rigs to sunken ships, life loves to settle on our stuff. Offshore mussel farming takes advantage of this phenomenon. Floating rope rigs are used to host mussels to maturity, which are fed entirely from […]
Original post on scicomm.xyz
scicomm.xyz
June 9, 2025 at 4:32 AM
In the ocean, if you build it, they will come. By "they" I mean the entire ecosystem! From oil rigs to sunken ships, life loves to settle on our stuff. Offshore mussel farming takes advantage of this phenomenon. Floating rope rigs are used to host mussels to maturity, which are fed entirely from […]
Reposted by soaproot
So, the Dutch cabinet just dissolved itself. It lasted much longer than anticipated and created more damage than what can be repaired in just a few weeks. Let’s hope for a more stable and more sensible government in the future. Latest polls still see the populists that have a history of running […]
Original post on mastodon.social
mastodon.social
June 3, 2025 at 8:16 AM
So, the Dutch cabinet just dissolved itself. It lasted much longer than anticipated and created more damage than what can be repaired in just a few weeks. Let’s hope for a more stable and more sensible government in the future. Latest polls still see the populists that have a history of running […]
Reposted by soaproot
This is a problem that all those clever AI/ML people should try to bring down the numbers in:
"Consider the class of Diophantine equations with at most 11 unknowns and
at most degree \\(1.63 \cdot 10^{63}\\). Hilbert’s Tenth Problem is unsolvable for this class: There is no algorithm that can […]
"Consider the class of Diophantine equations with at most 11 unknowns and
at most degree \\(1.63 \cdot 10^{63}\\). Hilbert’s Tenth Problem is unsolvable for this class: There is no algorithm that can […]
Original post on mathstodon.xyz
mathstodon.xyz
May 24, 2025 at 10:59 AM
This is a problem that all those clever AI/ML people should try to bring down the numbers in:
"Consider the class of Diophantine equations with at most 11 unknowns and
at most degree \\(1.63 \cdot 10^{63}\\). Hilbert’s Tenth Problem is unsolvable for this class: There is no algorithm that can […]
"Consider the class of Diophantine equations with at most 11 unknowns and
at most degree \\(1.63 \cdot 10^{63}\\). Hilbert’s Tenth Problem is unsolvable for this class: There is no algorithm that can […]
Reposted by soaproot
How do we compute a function f : (ℕ → ℕ) → ℕ abstractly?
This question goes back to Brouwer in the early 20th century, and was investigated by many people, including Kleene.
Think of the input α : ℕ → ℕ of the function f as a sequence of natural numbers.
So out of a sequence of natural […]
This question goes back to Brouwer in the early 20th century, and was investigated by many people, including Kleene.
Think of the input α : ℕ → ℕ of the function f as a sequence of natural numbers.
So out of a sequence of natural […]
Original post on mathstodon.xyz
mathstodon.xyz
May 20, 2025 at 8:13 PM
How do we compute a function f : (ℕ → ℕ) → ℕ abstractly?
This question goes back to Brouwer in the early 20th century, and was investigated by many people, including Kleene.
Think of the input α : ℕ → ℕ of the function f as a sequence of natural numbers.
So out of a sequence of natural […]
This question goes back to Brouwer in the early 20th century, and was investigated by many people, including Kleene.
Think of the input α : ℕ → ℕ of the function f as a sequence of natural numbers.
So out of a sequence of natural […]
The San Bruno BART train station seems to have (at some point in the past) declared war on pigeons. The pigeons are winning. (Present but not pictured: lots more pigeons)
May 18, 2025 at 5:13 PM
The San Bruno BART train station seems to have (at some point in the past) declared war on pigeons. The pigeons are winning. (Present but not pictured: lots more pigeons)